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A008308 Triangle of tangent numbers.

%I A008308 #15 Dec 17 2021 05:38:47
%S A008308 1,1,2,1,8,1,16,20,1,136,40,1,272,616,70,1,3968,2016,112,1,7936,28160,
%T A008308 5376,168,1,176896,135680,12432,240,1,353792,1805056,508640,25872,330,
%U A008308 1,11184128,11977856,1595264,49632,440,1,22368256,154918400,59835776
%N A008308 Triangle of tangent numbers.
%D A008308 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 259.
%e A008308 Triangle begins:
%e A008308     1;
%e A008308     1;
%e A008308     2,  1;
%e A008308     8,  1;
%e A008308    16, 20, 1;
%e A008308   136, 40, 1;
%e A008308   ...
%t A008308 T[n_, n_] = 1; T[n_, k_] /; 0 <= k <= n := T[n, k] = T[n - 1, k - 1] + k*(k + 1)*T[n - 1, k + 1]; T[_, _] = 0;
%t A008308 row[n_] := DeleteCases[Table[T[n, k], {k, 1, n}] , 0];
%t A008308 Array[row, 13] // Flatten (* _Jean-François Alcover_, Nov 09 2017 *)
%Y A008308 Essentially the same triangle as A059419, which is the main entry for this triangle.
%Y A008308 Row sums give A006229.
%K A008308 tabf,nonn,nice
%O A008308 1,3
%A A008308 _N. J. A. Sloane_
%E A008308 More terms from Larry Reeves (larryr(AT)acm.org), Feb 08 2001